On chiral symmetry breaking in a constant magnetic field in higher dimension

Chiral symmetry breaking in the Nambu–Jona-Lasinio model in a constant magnetic field is studied in spacetimes of dimension D>4. It is shown that a constant magnetic field can be characterized by [D−12] parameters. For the maximal number of nonzero field parameters, we show that there is an effective reduction of the spacetime dimension for fermions in the infrared region D→1+1 for even-dimensional spacetimes and D→0+1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions.